Deflection at Any Point on Cantilever Beam carrying Couple Moment at Free End Calculator

✖Moment of couple is equal to the product of either of forces and the perpendicular distance between the forces.ⓘ Moment of Couple [M_c]			+10% -10%
✖Distance x from Support is the length of a beam from the support to any point on the beam.ⓘ Distance x from Support [x]			+10% -10%
✖Elasticity modulus of Concrete (Ec) is the ratio of the applied stress to the corresponding strain.ⓘ Elasticity Modulus of Concrete [E]			+10% -10%
✖Area Moment of Inertia is a moment about the centroidal axis without considering mass.ⓘ Area Moment of Inertia [I]			+10% -10%

✖Deflection of Beam Deflection is the movement of a beam or node from its original position. It happens due to the forces and loads being applied to the body.ⓘ Deflection at Any Point on Cantilever Beam carrying Couple Moment at Free End [δ]

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Deflection at Any Point on Cantilever Beam carrying Couple Moment at Free End

Formula

`"δ" = (("M"_{"c"}*"x"^2)/(2*"E" *"I"))`

Example

`"1.496354mm"=(("85kN*m"*("1300mm")^2)/(2*"30000MPa" *"0.0016m⁴"))`

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Deflection at Any Point on Cantilever Beam carrying Couple Moment at Free End Solution

STEP 0: Pre-Calculation Summary

Formula Used

Deflection of Beam = ((Moment of Couple*Distance x from Support^2)/(2*Elasticity Modulus of Concrete *Area Moment of Inertia))
δ = ((M_c*x^2)/(2*E *I))
This formula uses 5 Variables

Variables Used

Deflection of Beam - (Measured in Meter) - Deflection of Beam Deflection is the movement of a beam or node from its original position. It happens due to the forces and loads being applied to the body.
Moment of Couple - (Measured in Newton Meter) - Moment of couple is equal to the product of either of forces and the perpendicular distance between the forces.
Distance x from Support - (Measured in Meter) - Distance x from Support is the length of a beam from the support to any point on the beam.
Elasticity Modulus of Concrete - (Measured in Pascal) - Elasticity modulus of Concrete (Ec) is the ratio of the applied stress to the corresponding strain.
Area Moment of Inertia - (Measured in Meter⁴) - Area Moment of Inertia is a moment about the centroidal axis without considering mass.

STEP 1: Convert Input(s) to Base Unit

Moment of Couple: 85 Kilonewton Meter --> 85000 Newton Meter (Check conversion here)
Distance x from Support: 1300 Millimeter --> 1.3 Meter (Check conversion here)
Elasticity Modulus of Concrete: 30000 Megapascal --> 30000000000 Pascal (Check conversion here)
Area Moment of Inertia: 0.0016 Meter⁴ --> 0.0016 Meter⁴ No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

δ = ((M_c*x^2)/(2*E *I)) --> ((85000*1.3^2)/(2*30000000000 *0.0016))

Evaluating ... ...

δ = 0.00149635416666667

STEP 3: Convert Result to Output's Unit

0.00149635416666667 Meter -->1.49635416666667 Millimeter (Check conversion here)

FINAL ANSWER

1.49635416666667 ≈ 1.496354 Millimeter <-- Deflection of Beam

(Calculation completed in 00.004 seconds)

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< 13 Cantilever Beam Calculators

Deflection at Any Point on Cantilever Beam carrying UDL

Go Deflection of Beam = ((Load per Unit Length*Distance x from Support^2)*(((Distance x from Support^2)+(6*Length of Beam^2)- (4*Distance x from Support*Length of Beam))/(24*Elasticity Modulus of Concrete*Area Moment of Inertia)))

Deflection of Cantilever Beam carrying Point Load at Any Point

Go Deflection of Beam = (Point Load*(Distance from Support A^2)*(3*Length of Beam-Distance from Support A))/(6*Elasticity Modulus of Concrete*Area Moment of Inertia)

Maximum Deflection of Cantilever Beam Carrying UVL with Maximum Intensity at Free End

Go Deflection of Beam = ((11*Uniformly Varying Load*(Length of Beam^4))/(120*Elasticity Modulus of Concrete*Area Moment of Inertia))

Deflection at Any Point on Cantilever Beam carrying Couple Moment at Free End

Go Deflection of Beam = ((Moment of Couple*Distance x from Support^2)/(2*Elasticity Modulus of Concrete *Area Moment of Inertia))

Maximum Deflection of Cantilever Beam carrying UVL with Maximum Intensity at Support

Go Deflection of Beam = (Uniformly Varying Load*(Length of Beam^4))/(30*Elasticity Modulus of Concrete*Area Moment of Inertia)

Maximum Deflection of Cantilever Beam carrying UDL

Go Deflection of Beam = (Load per Unit Length*(Length of Beam^4))/(8*Elasticity Modulus of Concrete*Area Moment of Inertia)

Slope at Free End of Cantilever Beam Carrying UVL with Maximum Intensity at Fixed End

Go Slope of Beam = ((Uniformly Varying Load*Length of Beam^3)/(24*Elasticity Modulus of Concrete*Area Moment of Inertia))

Maximum Deflection of Cantilever Beam with Couple Moment at Free End

Go Deflection of Beam = (Moment of Couple*(Length of Beam^2))/(2*Elasticity Modulus of Concrete*Area Moment of Inertia)

Slope at Free End of Cantilever Beam carrying UDL

Go Slope of Beam = ((Load per Unit Length*Length of Beam^3)/(6*Elasticity Modulus of Concrete*Area Moment of Inertia))

Slope at Free End of Cantilever Beam Carrying Concentrated Load at Any Point from Fixed End

Go Slope of Beam = ((Point Load*Distance x from Support^2)/(2*Elasticity Modulus of Concrete*Area Moment of Inertia))

Maximum Deflection of Cantilever Beam carrying Point Load at Free End

Go Deflection of Beam = (Point Load*(Length of Beam^3))/(3*Elasticity Modulus of Concrete*Area Moment of Inertia)

Slope at Free End of Cantilever Beam Carrying Couple at Free End

Go Slope of Beam = ((Moment of Couple*Length of Beam)/(Elasticity Modulus of Concrete*Area Moment of Inertia))

Slope at Free End of Cantilever Beam Carrying Concentrated Load at Free End

Go Slope of Beam = ((Point Load*Length of Beam^2)/(2*Elasticity Modulus of Concrete*Area Moment of Inertia))

Deflection at Any Point on Cantilever Beam carrying Couple Moment at Free End Formula

Deflection of Beam = ((Moment of Couple*Distance x from Support^2)/(2*Elasticity Modulus of Concrete *Area Moment of Inertia))
δ = ((M_c*x^2)/(2*E *I))

What is Beam Deflection?

The Deformation of a Beam is usually expressed in terms of its deflection from its original unloaded position. The deflection is measured from the original neutral surface of the beam to the neutral surface of the deformed beam. The configuration assumed by the deformed neutral surface is known as the elastic curve of the beam.

What is Moment of Couple?

The Moment of Couple is defined as the product of one of the two forces of a Couple and the perpendicular distance between their lines of action (called the arm of the Couple).

How to Calculate Deflection at Any Point on Cantilever Beam carrying Couple Moment at Free End?

Deflection at Any Point on Cantilever Beam carrying Couple Moment at Free End calculator uses Deflection of Beam = ((Moment of Couple*Distance x from Support^2)/(2*Elasticity Modulus of Concrete *Area Moment of Inertia)) to calculate the Deflection of Beam, The Deflection at Any Point on Cantilever Beam carrying Couple Moment at Free End formula is defined as the distance between its position before and after loading. Deflection of Beam is denoted by δ symbol.

How to calculate Deflection at Any Point on Cantilever Beam carrying Couple Moment at Free End using this online calculator? To use this online calculator for Deflection at Any Point on Cantilever Beam carrying Couple Moment at Free End, enter Moment of Couple (M_c), Distance x from Support (x), Elasticity Modulus of Concrete (E) & Area Moment of Inertia (I) and hit the calculate button. Here is how the Deflection at Any Point on Cantilever Beam carrying Couple Moment at Free End calculation can be explained with given input values -> 0.001496 = ((85000*1.3^2)/(2*30000000000 *0.0016)).

FAQ

What is Deflection at Any Point on Cantilever Beam carrying Couple Moment at Free End?

The Deflection at Any Point on Cantilever Beam carrying Couple Moment at Free End formula is defined as the distance between its position before and after loading and is represented as δ = ((M_c*x^2)/(2*E *I)) or Deflection of Beam = ((Moment of Couple*Distance x from Support^2)/(2*Elasticity Modulus of Concrete *Area Moment of Inertia)). Moment of couple is equal to the product of either of forces and the perpendicular distance between the forces, Distance x from Support is the length of a beam from the support to any point on the beam, Elasticity modulus of Concrete (Ec) is the ratio of the applied stress to the corresponding strain & Area Moment of Inertia is a moment about the centroidal axis without considering mass.

How to calculate Deflection at Any Point on Cantilever Beam carrying Couple Moment at Free End?

The Deflection at Any Point on Cantilever Beam carrying Couple Moment at Free End formula is defined as the distance between its position before and after loading is calculated using Deflection of Beam = ((Moment of Couple*Distance x from Support^2)/(2*Elasticity Modulus of Concrete *Area Moment of Inertia)). To calculate Deflection at Any Point on Cantilever Beam carrying Couple Moment at Free End, you need Moment of Couple (M_c), Distance x from Support (x), Elasticity Modulus of Concrete (E) & Area Moment of Inertia (I). With our tool, you need to enter the respective value for Moment of Couple, Distance x from Support, Elasticity Modulus of Concrete & Area Moment of Inertia and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Deflection of Beam?

In this formula, Deflection of Beam uses Moment of Couple, Distance x from Support, Elasticity Modulus of Concrete & Area Moment of Inertia. We can use 7 other way(s) to calculate the same, which is/are as follows -

Deflection of Beam = ((Load per Unit Length*Distance x from Support^2)*(((Distance x from Support^2)+(6*Length of Beam^2)- (4*Distance x from Support*Length of Beam))/(24*Elasticity Modulus of Concrete*Area Moment of Inertia)))
Deflection of Beam = (Point Load*(Distance from Support A^2)*(3*Length of Beam-Distance from Support A))/(6*Elasticity Modulus of Concrete*Area Moment of Inertia)
Deflection of Beam = (Point Load*(Length of Beam^3))/(3*Elasticity Modulus of Concrete*Area Moment of Inertia)
Deflection of Beam = (Load per Unit Length*(Length of Beam^4))/(8*Elasticity Modulus of Concrete*Area Moment of Inertia)
Deflection of Beam = (Uniformly Varying Load*(Length of Beam^4))/(30*Elasticity Modulus of Concrete*Area Moment of Inertia)
Deflection of Beam = ((11*Uniformly Varying Load*(Length of Beam^4))/(120*Elasticity Modulus of Concrete*Area Moment of Inertia))
Deflection of Beam = (Moment of Couple*(Length of Beam^2))/(2*Elasticity Modulus of Concrete*Area Moment of Inertia)

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